TY - GEN

T1 - The complement bimetric-dimension of corona graphs

AU - Rinurwati,

AU - Sundusia, Jafna Kamalia

AU - Haryadi, Tri Irvan

AU - Maharani, Fadillah Dian

N1 - Publisher Copyright:
© 2024 Author(s).

PY - 2024/2/2

Y1 - 2024/2/2

N2 - Let G be a connected graph, V (G) be a vertex set of G, d(u, v) be a length of shortest path between u, v ∈ V(G), and δ(u, v) be a length of longest path between u, v ∈ V(G). For every vertex u and an ordered subset S = {s1, s2, s3,.., sk} ⊆ V (G), let a and b of (a, b) be a pair k-tuple that is a = (d(u, s1), d (u, s2),.., d (u, sk)) and b = (δ (u, s1),δ (u, s2),.., δ(u, sk)). It has been stated that the subset S is called a bimetric-generator set of G if every two different vertices in G have distinct bimetric-representation with respect to S, and if cardinality of S is minimum then S is called bimetric-basis of G and its cardinality denoted by βb (G) that is bimetric-dimension of G. To develop the concept of bimetric-dimension, this research introduces a concept of complement bi-metric dimension. Subset S is called a complement bimetric-generator set of G if at least there are two vertices in G have the same complement bimetric representation with respect to S. If the cardinality of the such S is maximum then S called as complement bimetric basis of G and its number of vertices is complement bimetric-dimension of G, denoted by βb¯. It is also discussed in this research about a complement bimetric-dimension of corona product graphs. The complement bimetric-dimension of corona product graphs of two connected graphs G and H, βb¯(G ⊙ H), is βb¯(G ⊙ H) = (|V (G) - 1)(|V (H)| + 1) + βb¯(K1 + H), is influenced by the order of each graph and the complement bimetric-dimension of K1+H.

AB - Let G be a connected graph, V (G) be a vertex set of G, d(u, v) be a length of shortest path between u, v ∈ V(G), and δ(u, v) be a length of longest path between u, v ∈ V(G). For every vertex u and an ordered subset S = {s1, s2, s3,.., sk} ⊆ V (G), let a and b of (a, b) be a pair k-tuple that is a = (d(u, s1), d (u, s2),.., d (u, sk)) and b = (δ (u, s1),δ (u, s2),.., δ(u, sk)). It has been stated that the subset S is called a bimetric-generator set of G if every two different vertices in G have distinct bimetric-representation with respect to S, and if cardinality of S is minimum then S is called bimetric-basis of G and its cardinality denoted by βb (G) that is bimetric-dimension of G. To develop the concept of bimetric-dimension, this research introduces a concept of complement bi-metric dimension. Subset S is called a complement bimetric-generator set of G if at least there are two vertices in G have the same complement bimetric representation with respect to S. If the cardinality of the such S is maximum then S called as complement bimetric basis of G and its number of vertices is complement bimetric-dimension of G, denoted by βb¯. It is also discussed in this research about a complement bimetric-dimension of corona product graphs. The complement bimetric-dimension of corona product graphs of two connected graphs G and H, βb¯(G ⊙ H), is βb¯(G ⊙ H) = (|V (G) - 1)(|V (H)| + 1) + βb¯(K1 + H), is influenced by the order of each graph and the complement bimetric-dimension of K1+H.

UR - http://www.scopus.com/inward/record.url?scp=85184574671&partnerID=8YFLogxK

U2 - 10.1063/5.0193917

DO - 10.1063/5.0193917

M3 - Conference contribution

AN - SCOPUS:85184574671

T3 - AIP Conference Proceedings

BT - AIP Conference Proceedings

A2 - Anwar, Lathiful

A2 - Rahmadani, Desi

A2 - Cahyani, Denis Eka

A2 - Listiawan, Tomi

A2 - Rofiki, Imam

A2 - Darmawan, Puguh

A2 - Pahrany, Andi Daniah

PB - American Institute of Physics Inc.

T2 - 3rd International Conference on Mathematics and its Applications, ICoMathApp 2022

Y2 - 23 August 2022 through 24 August 2022

ER -